Doolittle has pitched his entire career in Oakland after playing collegiately at Virginia. He was an All-Star closer in 2014 and saved 22 games that year. Since then, he has finished just 26 games for the A’s but is instantly one of the best options to slide into the closer role.

Madson also has ample experience as a closer, logging 30-save seasons in 2011 with the Philadelphia Phillies and 2016 with Oakland. He returns to the National League East, where he spent the first nine years of his career, in Philly.

Manager Dusty Baker would not name a closer sight unseen, but general manager Mike Rizzo suggested that the goal was to name a closer to define some roles in the back end of the bullpen.

“I think that Dusty will stabilize the bullpen and set on one guy and kind of get a little rhythm back there and get guys comfortable in their roles,” Rizzo said. “It’s nice to have guys who have done it before, guys who have pitched in big games and pitched in playoff games.

“That had a lot to do with it.”

Rizzo explained that the deal began percolating around “one of the relievers” weeks ago. As the teams got closer to a deal, interest in both relievers became mutual until a deal was done.

“I think the ability and the stuff was important to us. They performed great throughout their careers, they performed really well this year,” Rizzo told the media on Sunday. “One’s left-handed, one’s right-handed. That gives us a little bit more balance in the bullpen. They’re both capable of getting out both lefty and right-handed hitters.

“They’re very versatile, no egos, they’re capable of pitching in the eighth or ninth inning, they’ve both done it. We’re really happy with the acquisition.”

Whoever gets first shot at the closer role has a chance to become the eighth player to record a save for the Nats this season. Treinen was the early choice, losing the gig after only a few weeks. Koda Glover and Shawn Kelley were inconsistent and are both on the disabled list.

Now is a chance to set a known deficiency right.

“We needed some help,” Baker said. “We got two quality guys and both of them have been closers at some point in time. They got what they wanted – some young players and Treinen – and I hate to give up Treinen, but you have to give up something to get something.

“We got two proven major leaguers. Both of them have been closers to shore up the back end of our bullpen so, hopefully, everybody can settle back into their roles and everybody can relax.”

Luzardo, 19, is a rookie-league lefty who has started three games for the Gulf Coast League Nationals. He has a 1.32 ERA in 13.2 innings pitched.

Neuse, 22, is a single-A third baseman for the Hagerstown Suns. He has a solid batting line of .291/.349/.469 in 77 games this season but is still a long way from contributing at the Major League level.